The increase in the cost of developing systems that operate according to predetermined specifications, such as government standards, has sparked a growth in the design and implementation of process control systems. These control systems typically incorporate process models that may predict, control, and control the performance of the system based on information reflecting the system's historical operations.
A process model may be a mathematical construct that reflects various characteristics of a target system. The model may be used to determine a dependent response variable based on one or more independent control variables. One known type of modeling system implemented in process control systems are neural networks. These types of systems are designed to mimic the operations of the human brain by determining the interaction between input and response variables based on a network of processing cells. The cells, commonly known as neurons, are generally arranged in layers, with each cell receiving inputs from a preceding layer and providing an output to a subsequent layer. The interconnections which transfer the inputs and outputs in a neural network are associated with a weight value that may be adjusted to allow the network to produce a predicted output value.
Neural networks may provide predicted response values based on historical data associated with the modeled system provided as the independent input variables to the network. The weights of the network are adjusted each time the historical data is provided as an input to allow the network to accurately predict the response variables. The predicted outputs are compared to actual response data of the system and weights are adjusted accordingly until a target response value is obtained.
In other traditional process control systems, the relationship between independent control variables and a dependent response variable is determined based on a mathematical function that reflects the relationship. These systems generally attempt to map the relationship using a single mapping function that is selected by a human operator. In most instances, however, a single function fails to accurately represent this relationship. For example, as shown in FIG. 1, a single function F, such as a quadratic function, does not accurately represent the actual relationship F′ between an exemplary control variable X and a response variable Y.
To address the inaccuracies associated with single function mapping, conventional process control systems attempt to reduce the range of control variables where the single function appears to accurately depict the relationship between a control and response variable. For example, as show in FIG. 1, the quadratic unction F may be accurate of the X and Y relationship in range R1. Although accurate, these conventional system require a user to define the ranges of the function representing the relationship between the two variables. Further, after a user has defined an appropriate range, another test run must be performed to allow the user to identify the next region in the mapped relationship that indicates a possible accurate relationship.
Although the conventional process of defining ranges and re-testing may eventually allow a relationship between a control and response variable to be mapped to a function, the process is time consuming, requires the input of a user who understands the relationship between the variables, and requires extensive processing and storage space. Also, as the complexity of the relationship increases (e.g., multiple control and response variables), the inefficiencies and inaccuracies of the conventional process control systems described above also increase. For example, there may be some instances where a conventional system may encounter a design space that includes a plurality of response and control variables that requires a three-dimensional, and beyond, mapping construct. Such abstract constructs may be beyond the capabilities of the processing system and/or users involved in mapping the relationships. Therefore, accurate complex mapping functions are unobtainable.
Methods, systems, and articles of manufacture consistent with certain features of the present invention are directed to solving one or more of the problems set forth above.